Abstract
Letf be a non-decreasing C1-function such that\(f > 0 on (0,\infty ), f(0) = 0, \int_1^\infty {1/\sqrt {F(t)} dt< \infty } \) andF(t)/f 2 a(t)→ 0 ast → ∞, whereF(t)=∫ t0 f(s) ds anda ∈ (0, 2]. We prove the existence of positive large solutions to the equationΔu +q(x)|Δu|a=p(x)f(u) in a smooth bounded domain Ω ⊂RN, provided thatp, q are non-negative continuous functions so that any zero ofp is surrounded by a surface strictly included in Ω on whichp is positive. Under additional hypotheses onp we deduce the existence of solutions if Ω is unbounded.
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Ghergu, M., Niculescu, C. & Rădulescu, V. Explosive solutions of elliptic equations with absorption and nonlinear gradient term. Proc. Indian Acad. Sci. (Math. Sci.) 112, 441–451 (2002). https://doi.org/10.1007/BF02829796
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DOI: https://doi.org/10.1007/BF02829796